College

What is the logarithmic form of [tex]$13^2=169$[/tex]?

A. [tex]\log _2 169=13[/tex]

B. [tex]\log _2 13=169[/tex]

C. [tex]\log _{13} 169=2[/tex]

D. [tex]\log _{13} 2=169[/tex]

Answer :

We start with the exponential equation:

[tex]$$13^2 = 169.$$[/tex]

Recall that in general if we have an equation of the form

[tex]$$b^x = y,$$[/tex]

it can be rewritten in its logarithmic form as

[tex]$$\log_b(y) = x.$$[/tex]

Here, identifying the components we have:

- Base [tex]$b = 13$[/tex],
- Exponent [tex]$x = 2$[/tex],
- Result [tex]$y = 169$[/tex].

Thus, writing [tex]$13^2=169$[/tex] in logarithmic form gives:

[tex]$$\log_{13}(169) = 2.$$[/tex]

This corresponds to the answer: [tex]$\log_{13} 169=2$[/tex].

Other Questions